Triangle angle bisector

Two or more lines are concurrent if there is a single point which lies on all of them. The three altitudes of a triangle (if taken as lines, not segments) are always concurrent, and their point of concurrency is called the orthocenter. The angle bisectors of a triangle are concurrent at a point equidistant from their sides, and the medians are concurrent two thirds of the way along each median from the vertex to the opposite side. The point of concurrency of the medians is the centroid. 

Reflection of a median of a triangle about the corresponding angle bisector. 

Figure 3.22 Bond bending, A0 = 6>nuciei - 6>nho, in CH2F—NH2 for C—F (circles, solid line), C—Hanti (squares, dotted line), and C—Hsyn (triangles, dotted line) bonds as the amine group is twisted from 0(lp—N—C—F) = 0° to 180° ( lp denotes the bisector of the H—N—H angle).

Consider Fig. 17 which shows an equilateral triangle having a point, P, within its perimeter. If we allow the line that bisects each apex angle and which extends to the opposing side to have a length of unity, then the distance along or parallel to each of these bisectors can be related to... 

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